Parte trigonométrica
[src]
/ /x\ \
| tan|-| |
| \2/ |
atan|-------------------------------|
| / 2/x\\|
| | 1 - tan |-|||
|/ 2/x\\ | \2/||
||1 + tan |-||*|1 + -----------||
|\ \2// | 2/x\||
| | 1 + tan |-|||
\ \ \2///
-------------------------------------
2
$$\frac{\operatorname{atan}{\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + 1\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)}}{2}$$
/ /x\ \
| 2*cot|-| |
| \2/ |
atan|------------------------------------|
| / / 2/x\\\|
| | 2*|-1 + cot |-||||
|/ 2/x\\ | \ \2//||
||1 + cot |-||*|2 + ----------------||
|\ \2// | 2/x\ ||
| | 1 + cot |-| ||
\ \ \2/ //
------------------------------------------
2
$$\frac{\operatorname{atan}{\left(\frac{2 \cot{\left(\frac{x}{2} \right)}}{\left(\frac{2 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} + 2\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)}}{2}$$
/ 1 \
atan|------------------------|
|/ 2 \ / pi\|
||2 + ------|*sec|x - --||
\\ sec(x)/ \ 2 //
------------------------------
2
$$\frac{\operatorname{atan}{\left(\frac{1}{\left(2 + \frac{2}{\sec{\left(x \right)}}\right) \sec{\left(x - \frac{\pi}{2} \right)}} \right)}}{2}$$
/ /x\ \
| cot|-| |
| \2/ |
atan|--------------------------------|
| / 2/x\\|
| | -1 + cot |-|||
|/ 2/x\\ | \2/||
||1 + cot |-||*|1 + ------------||
|\ \2// | 2/x\ ||
| | 1 + cot |-| ||
\ \ \2/ //
--------------------------------------
2
$$\frac{\operatorname{atan}{\left(\frac{\cot{\left(\frac{x}{2} \right)}}{\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} + 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)}}{2}$$
/ / pi\ \
|cos|x - --| |
| \ 2 / |
atan|------------|
\2 + 2*cos(x)/
------------------
2
$$\frac{\operatorname{atan}{\left(\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{2 \cos{\left(x \right)} + 2} \right)}}{2}$$
/ sin(x) \
atan|------------|
\2 + 2*cos(x)/
------------------
2
$$\frac{\operatorname{atan}{\left(\frac{\sin{\left(x \right)}}{2 \cos{\left(x \right)} + 2} \right)}}{2}$$
/ 1 \
atan|--------------------------|
| / 1 \ / pi\|
|2*|1 + ------|*sec|x - --||
\ \ sec(x)/ \ 2 //
--------------------------------
2
$$\frac{\operatorname{atan}{\left(\frac{1}{2 \left(1 + \frac{1}{\sec{\left(x \right)}}\right) \sec{\left(x - \frac{\pi}{2} \right)}} \right)}}{2}$$
/ sin(x) \
atan|-------------------|
| / / pi\\|
|2*|1 + sin|x + --|||
\ \ \ 2 ///
-------------------------
2
$$\frac{\operatorname{atan}{\left(\frac{\sin{\left(x \right)}}{2 \left(\sin{\left(x + \frac{\pi}{2} \right)} + 1\right)} \right)}}{2}$$
/ sin(x) \
atan|-----------------|
| / pi\|
|2 + 2*sin|x + --||
\ \ 2 //
-----------------------
2
$$\frac{\operatorname{atan}{\left(\frac{\sin{\left(x \right)}}{2 \sin{\left(x + \frac{\pi}{2} \right)} + 2} \right)}}{2}$$
/ /x\ \
| 2*tan|-| |
| \2/ |
atan|-----------------------------------|
| / / 2/x\\\|
| | 2*|1 - tan |-||||
|/ 2/x\\ | \ \2//||
||1 + tan |-||*|2 + ---------------||
|\ \2// | 2/x\ ||
| | 1 + tan |-| ||
\ \ \2/ //
-----------------------------------------
2
$$\frac{\operatorname{atan}{\left(\frac{2 \tan{\left(\frac{x}{2} \right)}}{\left(\frac{2 \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + 2\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)}}{2}$$
/ / pi\ \
| cos|x - --| |
| \ 2 / |
atan|--------------|
\2*(1 + cos(x))/
--------------------
2
$$\frac{\operatorname{atan}{\left(\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{2 \left(\cos{\left(x \right)} + 1\right)} \right)}}{2}$$
/ 1 \
atan|------------------------|
|/ 2 \ |
||2 + -----------|*csc(x)|
|| /pi \| |
|| csc|-- - x|| |
\\ \2 // /
------------------------------
2
$$\frac{\operatorname{atan}{\left(\frac{1}{\left(2 + \frac{2}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right) \csc{\left(x \right)}} \right)}}{2}$$
/ 1 \
atan|--------------------------|
| / 1 \ |
|2*|1 + -----------|*csc(x)|
| | /pi \| |
| | csc|-- - x|| |
\ \ \2 // /
--------------------------------
2
$$\frac{\operatorname{atan}{\left(\frac{1}{2 \left(1 + \frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right) \csc{\left(x \right)}} \right)}}{2}$$
/ 1 \
atan|-------------------|
|/ 2 \ |
||2 + ------|*csc(x)|
\\ sec(x)/ /
-------------------------
2
$$\frac{\operatorname{atan}{\left(\frac{1}{\left(2 + \frac{2}{\sec{\left(x \right)}}\right) \csc{\left(x \right)}} \right)}}{2}$$
atan(1/((2 + 2/sec(x))*csc(x)))/2